Syllogism

SQUARE OF OPPOSITION

The square of opposition is a diagram that represents the relation between four propositions. These propositions can be A, E, I and O. Where,

A- All

E- No

I- Some

O- Some not

For example,

All are red - A

No is red - E

Some are red - I

Some are not red - O

The relationship between these propositions (with the help of square of opposition) is given below:

   The definition of these relations can be easily understood with the help of the following table:

Relation	True	False
Contrary	XX	√√
Sub-Contrary	√√	XX
Contradictory	XX	XX
Sub-Alteration	√√	√√

The above table shows that

ü  In case of Contrary, both statements can’t be true but both can be false at same time.

ü  In case of Sub-Contrary, both statements can be true but both can’t be false at same time.

ü  In case of Contradictory, both statements can’t be true or false at same time i.e. if one is true other will be false.

ü  In case of Sub-Alteration, both statements can be true and false at same time.

UGC NET Previous Years Questions:

Q) Among the following propositions two are related in such a way that they cannot both be true but can be false. Select the code states those two propositions (Jan 2017)
Propositions:

a.      Every student is attentive

b.      Some students are attentive

c.       Students are never attentive

d.     Some students are not attentive

Codes:

1.      (a) and (b)

2.      (a) and (c)

3.      (b) and (c)

4.      (c) and (d)

Answer: (2)

Description:  This is definition for contrary i.e. both can’t be true but both can be false. The contrary relation exist between A and E. We can also observe from statements that statement a is A (every), statement b (some) is I, statement c (never) is E, statement d (some not) is O. The contrary relation is between statement a and c.

 Thus, correct option is 2.